Restricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers
نویسندگان
چکیده
In 1985 Simion and Schmidt showed that the number of permutations in Sn which avoid 132, 213, and 123 is equal to the Fibonacci number Fn+1. We use generating function and bijective techniques to give other sets of pattern-avoiding permutations which can be enumerated in terms of Fibonacci or k-generalized Fibonacci numbers.
منابع مشابه
Restricted Permutations Related to Fibonacci Numbers and k-Generalized Fibonacci Numbers
A permutation π ∈ Sn is said to avoid a permutation σ ∈ Sk whenever π contains no subsequence with all of the same pairwise comparisons as σ. In 1985 Simion and Schmidt showed that the number of permutations in Sn which avoid 123, 132, and 213 is the Fibonacci number Fn+1. In this paper we generalize this result in two ways. We first show that the number of permutations which avoid 132, 213, an...
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